WO2023228371A1 - Information processing device, information processing method, and program - Google Patents

Information processing device, information processing method, and program Download PDF

Info

Publication number
WO2023228371A1
WO2023228371A1 PCT/JP2022/021605 JP2022021605W WO2023228371A1 WO 2023228371 A1 WO2023228371 A1 WO 2023228371A1 JP 2022021605 W JP2022021605 W JP 2022021605W WO 2023228371 A1 WO2023228371 A1 WO 2023228371A1
Authority
WO
WIPO (PCT)
Prior art keywords
kernel function
function
information processing
event
processor
Prior art date
Application number
PCT/JP2022/021605
Other languages
French (fr)
Japanese (ja)
Inventor
秀明 金
哲也 杵渕
太一 浅見
Original Assignee
日本電信電話株式会社
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 日本電信電話株式会社 filed Critical 日本電信電話株式会社
Priority to PCT/JP2022/021605 priority Critical patent/WO2023228371A1/en
Publication of WO2023228371A1 publication Critical patent/WO2023228371A1/en

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N7/00—Computing arrangements based on specific mathematical models

Definitions

  • One aspect of the present invention relates to an information processing device, an information processing method, and a program that estimate the probability of occurrence of an event (intensity function) with respect to a covariate based on data regarding an event occurrence position and a covariate.
  • This invention was made in view of the above-mentioned circumstances, and its purpose is to provide a technology capable of estimating an intensity function for a covariate using a Bayesian estimation method using a Gaussian process as a prior distribution. be.
  • An information processing device includes a processor and a storage unit.
  • the storage unit includes a first storage area and a first storage area.
  • the first storage area stores event occurrence data regarding the occurrence position of the event to be analyzed.
  • the second storage area stores covariate data observed within the event observation area.
  • the processor includes a kernel function specifying section, a calculation method specifying section, and an intensity function estimating section.
  • the kernel function designation unit accepts designation of a kernel function in a Gaussian process.
  • the calculation method designation unit accepts designation of a calculation method for the equivalent kernel function.
  • the intensity function estimation unit calculates an equivalent kernel function based on a specified kernel function and calculation method, and estimates an intensity function for a covariate using the calculated equivalent kernel function.
  • FIG. 1 is a functional block diagram showing an example of an information processing device according to an embodiment.
  • FIG. 2 is a functional block diagram showing an example of the information processing device 1 shown in FIG. 1.
  • FIG. 3 is a flowchart showing an example of a processing procedure of the information processing device 1 shown in FIG.
  • FIG. 1 is a functional block diagram showing an example of an information processing device according to an embodiment.
  • the information processing device 1 is a computer including a processor and a memory.
  • the information processing device 1 includes a processor 11, an input/output interface 12, and a storage unit 13.
  • the processor 11, the input/output interface 12, and the storage unit 13 are communicably connected to each other via a bus.
  • Processor 11 controls information processing device 1 .
  • the processor 11 is an arithmetic processing device such as a CPU (Central Processing Unit) or an MPU (Micro Processing Unit).
  • the input/output interface 12 is an interface that allows information to be sent and received between the input device 2 and the output device 3.
  • the input/output interface 12 may include a wired or wireless communication interface. That is, the information processing device 1, the input device 2, and the output device 3 may transmit and receive information via a network such as a LAN or the Internet.
  • the storage unit 13 is a storage medium.
  • the storage unit 13 includes, for example, a non-volatile memory that can be written to and read from at any time such as an HDD (Hard Disk Drive) or an SSD (Solid State Drive), a non-volatile memory such as a ROM (Read Only Memory), a RAM (Random Access Memory), etc. It is configured in combination with volatile memory.
  • the storage unit 13 includes a program storage area and a data storage area.
  • the program storage area stores application programs necessary for executing various processes in addition to the OS (Operating System) and middleware.
  • the input device 2 includes, for example, a keyboard, a pointing device, etc. for an owner of the information processing device 1 (for example, an assignee, a manager, a supervisor, etc.) to input instructions to the information processing device 1. Furthermore, the input device 2 may include a reader for reading data to be stored in the storage unit 13 from a memory medium such as a USB memory, and a disk device for reading such data from a disk medium. Furthermore, the input device 2 may include an image scanner.
  • the output device 3 includes a display that displays output data to be presented to the owner from the information processing device 1, a printer that prints the output data, and the like.
  • the output device 3 also includes a writer for writing data to be input into another information processing device 1 such as a PC or a smartphone onto a memory medium such as a USB memory, or a disk for writing such data onto a disk medium. may include a device.
  • FIG. 2 is a functional block diagram showing an example of the information processing device 1 shown in FIG. 1.
  • the storage unit 13 stores a program 10 that causes the processor 11 to function as the information processing device 1.
  • the storage unit 13 includes a first storage area 131, a second storage area 132, and a third storage area 133.
  • the first storage area 131 stores event occurrence data 100.
  • the event occurrence data 100 is data regarding the occurrence position of the event to be analyzed, and includes at least the number of observed events, a series of event positions, and an observation area.
  • the second storage area 132 stores covariate data 101 observed within the observation area of the event to be analyzed.
  • the third storage area 133 stores the intensity function distribution 105 calculated by the processor 11.
  • the processor 11 includes a kernel function designation unit 102, a calculation method designation unit 103, an intensity function estimation unit 112, and an output control unit 114 as processing functions according to the embodiment.
  • the kernel function designation unit 102, the calculation method designation unit 103, the intensity function estimation unit 112, and the output control unit 114 are functional processes realized by the calculation processing of the processor 11 based on the program 10.
  • the kernel function designation unit 102 accepts designation of a kernel function in a Gaussian process.
  • the kernel function is specified by the user by operating the input device 2, for example.
  • the calculation method designation unit 103 accepts designation of the calculation method of the equivalent kernel function.
  • the calculation method may also be specified by the user operating the input device 2, for example.
  • the intensity function estimation unit 112 calculates an equivalent kernel function based on the specified kernel function and calculation method. Furthermore, the intensity function estimating unit 112 uses the calculated equivalent kernel function to estimate an intensity function for the covariate.
  • the intensity function distribution 105 is stored in the third storage area 133.
  • the output control unit 114 outputs the intensity function distribution 105 to the output device 3 via the input/output interface 12.
  • the output device 3 visualizes and displays the calculated intensity function distribution 105 on, for example, a display.
  • the processor 11 mainly executes the processes (1) to (4) to realize the estimation of the intensity function for the covariate based on the Bayesian estimation method using a Gaussian process as the prior distribution.
  • the square of that variable is defined as the intensity function.
  • the estimated value of the square root of the intensity function that maximizes the posterior probability is given as a solution to an N-element simultaneous equation, where N is the number of observed data. This can be expressed as the representer theorem holds. This fact makes it easy to numerically solve the estimate of the square root of the intensity function.
  • FIG. 3 is a flowchart showing an example of the processing procedure of the information processing device 1 shown in FIG.
  • the processor 11 accepts a user's designation of a kernel function in a Gaussian process (step SST21).
  • the processor 11 accepts the user's designation of the method for calculating the equivalent kernel function (step SST22).
  • the processor 11 calculates an equivalent kernel function based on the specified kernel function and calculation method (step ST23). Furthermore, the processor 11 estimates the intensity function for the covariate using the calculated equivalent kernel function (step S24).
  • the event occurrence data includes the following (A), (B), and (C).
  • the number of dimensions of the space in which an event occurs is arbitrary; for example, one dimension may be time, two dimensions may be geographical space, and three dimensions may be space and time.
  • the covariate data observed within the event observation region T is a function that outputs the covariate by inputting an arbitrary point (formula (D)) within the observation region (formula (C)). (Equation (E)).
  • Equation (E) In many applications, information about the covariates is only available on a finite number of points within the observation region (Equation (C)). In that case, it is assumed that the function (formula (E)) is constructed using an interpolation technique such as a regression model or kriging.
  • the kernel function in the Gaussian process To use the Gaussian process, specify a function called the kernel function that determines the smoothness of the function to be modeled. Also specify the values of parameters (hyperparameters) included in the function. Note that the function to be modeled in the embodiment is an intensity function for a covariate. The kernel function for arbitrary two points (formula (F)) in the covariate space is expressed as (formula (G)).
  • Equation (1) An example of a kernel function is the Gaussian kernel given by equation (1).
  • Equation (2) which is expressed by the inner product of a finite-dimensional feature mapping vector (Equation (H)).
  • a method for calculating equivalent kernel function is given as input.
  • the method for calculating the equivalent kernel function includes the type of calculation method and the Monte Carlo integration score (formula (I)).
  • type 1 the options for the type of calculation method are type 1 and type 2, and type 2 can only be selected when the kernel function is given by the inner product of finite-dimensional feature mapping vectors.
  • the processor 11 calculates an equivalent kernel function (formula (J)).
  • the processor 11 uses the equivalent kernel function (J) to estimate the intensity function (formula (K)) for the covariate.
  • Equation (J) the equivalent kernel function (Equation (J)) is defined as a solution to the integral equation of Equation (3).
  • equation (4) is obtained by approximating the integral part by Monte Carlo integration.
  • the present invention is not limited to the above embodiments as they are.
  • the selection of the kernel function is not limited to equation (1) or equation (2).
  • the present invention can be embodied by modifying the constituent elements within the scope of the embodiments at the implementation stage.
  • various inventions can be formed by appropriately combining the plurality of components disclosed in the above embodiments. For example, some components may be deleted from all the components shown in the embodiments. Furthermore, components from different embodiments may be combined as appropriate.

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Software Systems (AREA)
  • General Physics & Mathematics (AREA)
  • Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Artificial Intelligence (AREA)
  • Data Mining & Analysis (AREA)
  • Computing Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Medical Informatics (AREA)
  • Algebra (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Complex Calculations (AREA)

Abstract

An information processing device according to one aspect of this invention comprises a processor and a storage unit. The storage unit comprises a first storage area and a first storage area. The first storage area stores event occurrence data about a location of occurrence of an event to be analyzed. A second storage area stores covariate data observed in an observation area of the event. The processor has a kernel function designation unit, a calculation method designation unit, and an intensity function estimation unit. The kernel function designation unit accepts designation of a kernel function in a Gaussian process. The calculation method designation unit accepts designation of a calculation method of an equivalent kernel function. The intensity function estimation unit calculates an equivalent kernel function on the basis of the specified kernel function and calculation method, and estimates an intensity function with respect to the covariate using the calculated equivalent kernel function.

Description

情報処理装置、情報処理方法、およびプログラムInformation processing device, information processing method, and program
　この発明の一態様は、イベントの発生位置と共変量に関するデータに基づいて、共変量に対するイベントの発生確率（強度関数）を推定する情報処理装置、情報処理方法、およびプログラムに関する。 One aspect of the present invention relates to an information processing device, an information processing method, and a program that estimate the probability of occurrence of an event (intensity function) with respect to a covariate based on data regarding an event occurrence position and a covariate.
　任意の点で共変量が定義された空間において、点事象（以後イベントと表記する）が確率的に発生する状況を考える。この状況は、例えば、（空間，共変量，観測データ）＝（緯度／経度，群衆密度，事故イベントの発生位置）などとして表現することができる。共変量に対するイベントの発生確率（強度関数とも称される）を推定する技術として、カーネル密度推定法を利用した技術が知られている（例えば、非特許文献１を参照）。 Consider a situation in which point events (hereinafter referred to as events) occur stochastically in a space where covariates are defined at arbitrary points. This situation can be expressed, for example, as (space, covariates, observed data) = (latitude/longitude, crowd density, location of accident event). As a technique for estimating the probability of occurrence of an event (also referred to as an intensity function) with respect to a covariate, a technique using a kernel density estimation method is known (see, for example, Non-Patent Document 1).
　ところで、近年、カーネル密度推定法よりも高い精度を得られる手法が報告された。例えば、ガウス過程を事前分布とするベイズ推定法が、カーネル密度推定法よりも高い精度を達成することが知られている（例えば、非特許文献２，３を参照）。 By the way, in recent years, a method that can obtain higher accuracy than the kernel density estimation method has been reported. For example, it is known that a Bayesian estimation method using a Gaussian process as a prior distribution achieves higher accuracy than a kernel density estimation method (see, for example, Non-Patent Documents 2 and 3).
　共変量に対する強度関数を推定するのにカーネル密度推定法を用いる技術は知られている。ところが、カーネル密度推定法よりも高い精度を期待し得る、ガウス過程を事前分布とするベイズ推定法を用いることのできる技術は未だ知られていない。 Techniques using kernel density estimation to estimate intensity functions for covariates are known. However, there is still no known technology that can use a Bayesian estimation method using a Gaussian process as a prior distribution, which can be expected to have higher accuracy than the kernel density estimation method.
　この発明は上記事情に着目してなされたもので、その目的は、ガウス過程を事前分布とするベイズ推定法を用いて、共変量に対する強度関数を推定することの可能な技術を提供することにある。 This invention was made in view of the above-mentioned circumstances, and its purpose is to provide a technology capable of estimating an intensity function for a covariate using a Bayesian estimation method using a Gaussian process as a prior distribution. be.
　この発明の一態様に係る情報処理装置は、プロセッサおよび記憶部を備える。記憶部は、第１記憶領域と、第１記憶領域を備える。第１記憶領域は、解析対象のイベントの発生位置に関するイベント発生データを記憶する。第２記憶領域は、イベントの観測領域内で観測された共変量データを記憶する。プロセッサは、カーネル関数指定部と、算出方法指定部と、強度関数推定部とを具備する。カーネル関数指定部は、ガウス過程におけるカーネル関数の指定を受け付ける。算出方法指定部は、等価カーネル関数の算出方法の指定を受け付ける。強度関数推定部は、指定されたカーネル関数および算出方法に基づいて等価カーネル関数を算出し、当該算出された等価カーネル関数を利用して共変量に対する強度関数を推定する。 An information processing device according to one aspect of the present invention includes a processor and a storage unit. The storage unit includes a first storage area and a first storage area. The first storage area stores event occurrence data regarding the occurrence position of the event to be analyzed. The second storage area stores covariate data observed within the event observation area. The processor includes a kernel function specifying section, a calculation method specifying section, and an intensity function estimating section. The kernel function designation unit accepts designation of a kernel function in a Gaussian process. The calculation method designation unit accepts designation of a calculation method for the equivalent kernel function. The intensity function estimation unit calculates an equivalent kernel function based on a specified kernel function and calculation method, and estimates an intensity function for a covariate using the calculated equivalent kernel function.
　この発明の一態様によれば、共変量に対する強度関数を、ガウス過程を事前分布とするベイズ推定法に基づいて推定することの可能な技術を提供することができる。 According to one aspect of the present invention, it is possible to provide a technique capable of estimating an intensity function for a covariate based on a Bayesian estimation method using a Gaussian process as a prior distribution.
図１は、実施形態に係わる情報処理装置の一例を示す機能ブロック図である。FIG. 1 is a functional block diagram showing an example of an information processing device according to an embodiment. 図２は、図１に示される情報処理装置１の一例を示す機能ブロック図である。FIG. 2 is a functional block diagram showing an example of the information processing device 1 shown in FIG. 1. As shown in FIG. 図３は、図１に示される情報処理装置１の処理手順の一例を示すフローチャートである。FIG. 3 is a flowchart showing an example of a processing procedure of the information processing device 1 shown in FIG.
　以下、図面を参照してこの発明に係わる実施形態を説明する。　
　＜構成＞
　図１は、実施形態に係わる情報処理装置の一例を示す機能ブロック図である。　
　情報処理装置１は、プロセッサおよびメモリを備えるコンピュータである。情報処理装置１は、プロセッサ１１、入出力インタフェース１２、及び記憶部１３を備える。プロセッサ１１、入出力インタフェース１２、及び記憶部１３は、バスを介して互いに通信可能に接続される。　
　プロセッサ１１は、情報処理装置１を制御する。プロセッサ１１は、ＣＰＵ（Central Processing Unit）、あるいはＭＰＵ（Micro Processing Unit）などの演算処理デバイスである。 Embodiments of the present invention will be described below with reference to the drawings.
<Configuration>
FIG. 1 is a functional block diagram showing an example of an information processing device according to an embodiment.
The information processing device 1 is a computer including a processor and a memory. The information processing device 1 includes a processor 11, an input/output interface 12, and a storage unit 13. The processor 11, the input/output interface 12, and the storage unit 13 are communicably connected to each other via a bus.
Processor 11 controls information processing device 1 . The processor 11 is an arithmetic processing device such as a CPU (Central Processing Unit) or an MPU (Micro Processing Unit).
　入出力インタフェース１２は、入力装置２及び出力装置３との間で情報の送受信を可能にするインタフェースである。入出力インタフェース１２は、有線又は無線の通信インタフェースを備えてもよい。すなわち、情報処理装置１と入力装置２及び出力装置３とは、ＬＡＮやインターネット等のネットワークを経由して情報の送受信を行ってもよい。 The input/output interface 12 is an interface that allows information to be sent and received between the input device 2 and the output device 3. The input/output interface 12 may include a wired or wireless communication interface. That is, the information processing device 1, the input device 2, and the output device 3 may transmit and receive information via a network such as a LAN or the Internet.
　記憶部１３は、記憶媒体である。記憶部１３は、例えばＨＤＤ（Hard DiskDrive）又はＳＳＤ（Solid StateDrive）等の随時書込み及び読出し可能な不揮発性メモリと、ＲＯＭ（Read Only Memory）等の不揮発性メモリと、ＲＡＭ（Random Access Memory）等の揮発性メモリとを組み合わせて構成される。記憶部１３は、記憶領域に、プログラム記憶領域と、データ記憶領域とを備える。プログラム記憶領域は、ＯＳ（OperatingSystem）やミドルウェアに加えて、各種処理を実行するために必要なアプリケーションプログラムを格納する。 The storage unit 13 is a storage medium. The storage unit 13 includes, for example, a non-volatile memory that can be written to and read from at any time such as an HDD (Hard Disk Drive) or an SSD (Solid State Drive), a non-volatile memory such as a ROM (Read Only Memory), a RAM (Random Access Memory), etc. It is configured in combination with volatile memory. The storage unit 13 includes a program storage area and a data storage area. The program storage area stores application programs necessary for executing various processes in addition to the OS (Operating System) and middleware.
　入力装置２は、例えば、情報処理装置１の所有者（例えば、割当者、管理者、又は監督者等）が情報処理装置１に対して指示を入力するためのキーボードやポインティングデバイス等を含む。また、入力装置２は、記憶部１３に格納するべきデータを、ＵＳＢメモリ等のメモリ媒体から読み出すためのリーダや、そのようなデータをディスク媒体から読み出すためのディスク装置を含み得る。さらに入力装置２はイメージスキャナを含んでもよい。 The input device 2 includes, for example, a keyboard, a pointing device, etc. for an owner of the information processing device 1 (for example, an assignee, a manager, a supervisor, etc.) to input instructions to the information processing device 1. Furthermore, the input device 2 may include a reader for reading data to be stored in the storage unit 13 from a memory medium such as a USB memory, and a disk device for reading such data from a disk medium. Furthermore, the input device 2 may include an image scanner.
　出力装置３は、情報処理装置１から所有者に提示するべき出力データを表示するディスプレイや、それを印刷するプリンタ等を含む。また、出力装置３は、ＰＣやスマートフォン等の他の情報処理装置１に入力するべきデータを、ＵＳＢメモリ等のメモリ媒体に書き込むためのライタや、そのようなデータをディスク媒体に書き込むためのディスク装置を含み得る。 The output device 3 includes a display that displays output data to be presented to the owner from the information processing device 1, a printer that prints the output data, and the like. The output device 3 also includes a writer for writing data to be input into another information processing device 1 such as a PC or a smartphone onto a memory medium such as a USB memory, or a disk for writing such data onto a disk medium. may include a device.
　図２は、図１に示される情報処理装置１の一例を示す機能ブロック図である。図２において、記憶部１３は、プロセッサ１１を情報処理装置１として機能させるプログラム１０を記憶する。さらに、記憶部１３は、第１記憶領域１３１、第２記憶領域１３２、および、第３記憶領域１３３を備える。　
　第１記憶領域１３１は、イベント発生データ１００を記憶する。イベント発生データ１００は、解析対象のイベントの発生位置に関するデータであり、観測されたイベントの回数と、イベント位置の系列と、観測領域とを少なくとも含む。　
　第２記憶領域１３２は、解析対象のイベントの観測領域内で観測された共変量データ１０１を記憶する。　
　第３記憶領域１３３は、プロセッサ１１により算出された強度関数分布１０５を記憶する。 FIG. 2 is a functional block diagram showing an example of the information processing device 1 shown in FIG. 1. As shown in FIG. In FIG. 2, the storage unit 13 stores a program 10 that causes the processor 11 to function as the information processing device 1. Furthermore, the storage unit 13 includes a first storage area 131, a second storage area 132, and a third storage area 133.
The first storage area 131 stores event occurrence data 100. The event occurrence data 100 is data regarding the occurrence position of the event to be analyzed, and includes at least the number of observed events, a series of event positions, and an observation area.
The second storage area 132 stores covariate data 101 observed within the observation area of the event to be analyzed.
The third storage area 133 stores the intensity function distribution 105 calculated by the processor 11.
　プロセッサ１１は、実施形態に係わる処理機能として、カーネル関数指定部１０２、算出方法指定部１０３、強度関数推定部１１２、および、出力制御部１１４を備える。カーネル関数指定部１０２、算出方法指定部１０３、強度関数推定部１１２、および、出力制御部１１４は、プログラム１０に基づくプロセッサ１１の演算処理により実現される機能プロセスである。 The processor 11 includes a kernel function designation unit 102, a calculation method designation unit 103, an intensity function estimation unit 112, and an output control unit 114 as processing functions according to the embodiment. The kernel function designation unit 102, the calculation method designation unit 103, the intensity function estimation unit 112, and the output control unit 114 are functional processes realized by the calculation processing of the processor 11 based on the program 10.
　カーネル関数指定部１０２は、ガウス過程におけるカーネル関数の指定を受け付ける。カーネル関数は、例えば入力装置２を操作することで、ユーザにより指定される。　
　算出方法指定部１０３は、等価カーネル関数の算出方法の指定を受け付ける。算出方法も、例えば入力装置２を操作するユーザにより指定されてよい。　 The kernel function designation unit 102 accepts designation of a kernel function in a Gaussian process. The kernel function is specified by the user by operating the input device 2, for example.
The calculation method designation unit 103 accepts designation of the calculation method of the equivalent kernel function. The calculation method may also be specified by the user operating the input device 2, for example.
　強度関数推定部１１２は、指定されたカーネル関数と算出方法とに基づいて、等価カーネル関数を算出する。さらに、強度関数推定部１１２は、この算出された等価カーネル関数を、利用して共変量に対する強度関数を推定する。強度関数分布１０５は、第３記憶領域１３３に記憶される。 The intensity function estimation unit 112 calculates an equivalent kernel function based on the specified kernel function and calculation method. Furthermore, the intensity function estimating unit 112 uses the calculated equivalent kernel function to estimate an intensity function for the covariate. The intensity function distribution 105 is stored in the third storage area 133.
　出力制御部１１４は、強度関数分布１０５を入出力インタフェース１２を介して出力装置３に出力する。出力装置３は、算出された強度関数分布１０５を例えばディスプレイに可視化して表示する。 The output control unit 114 outputs the intensity function distribution 105 to the output device 3 via the input/output interface 12. The output device 3 visualizes and displays the calculated intensity function distribution 105 on, for example, a display.
　次に、上記構成における作用を説明する。
　＜作用＞
　（概要）
　先ず、作用の概要について説明する。実施形態では、プロセッサ１１により、主に（１）～（４）の処理を実行することで、ガウス過程を事前分布とするベイズ推定法に基づく共変量に対する強度関数の推定を実現する。 Next, the operation of the above configuration will be explained.
<Effect>
(overview)
First, an overview of the action will be explained. In the embodiment, the processor 11 mainly executes the processes (1) to (4) to realize the estimation of the intensity function for the covariate based on the Bayesian estimation method using a Gaussian process as the prior distribution.
　（１）共変量空間において定義されたガウス過程に従う変数に対し、その変数の２乗を強度関数と定義する。このようにすると、事後確率を最大化する強度関数の平方根の推定値（最大事後確率推定値あるいはＭＡＰ推定値）は、観測データの個数をＮとして、Ｎ元連立方程式の解として与えられる。これを、リプレゼンター定理が成り立つ、と表現することができる。この事実から、強度関数の平方根の推定値を数値的に解くことが容易になる。 (1) For a variable that follows a Gaussian process defined in the covariate space, the square of that variable is defined as the intensity function. In this way, the estimated value of the square root of the intensity function that maximizes the posterior probability (maximum posterior probability estimated value or MAP estimated value) is given as a solution to an N-element simultaneous equation, where N is the number of observed data. This can be expressed as the representer theorem holds. This fact makes it easy to numerically solve the estimate of the square root of the intensity function.
　（２）強度関数の平方根の推定誤差をラプラス近似により算出する。すなわち、強度関数の平方根が従う対数事後確率分布のＭＡＰ推定値におけるヘッセ行列を計算する。そして、当該ヘッセ行列の逆行列に－１を乗算したものを強度関数平方根の推定値の共分散行列とする。 (2) Calculate the estimation error of the square root of the intensity function using Laplace approximation. That is, the Hessian matrix of the MAP estimate of the logarithmic posterior probability distribution followed by the square root of the intensity function is calculated. Then, the inverse matrix of the Hessian matrix multiplied by -1 is used as the covariance matrix of the estimated value of the square root of the intensity function.
　（３）（２）のラプラス近似のもとで、強度関数の推定値が従うガンマ分布が得られる。この推定値に関する確率分布を得ることが、強度関数推定の最終目標となる。　
　（４）強度関数の推定に必要なハイパーパラメータを経験ベイズ法に基づき観測データから推定する。なお、経験ベイズ法とは周辺尤度を最大化するハイパーパラメータを推定値とする手法である。ハイパーパラメータの代表例として、ガウス過程におけるカーネル関数のパラメータなどが挙げられる。 (3) Under the Laplace approximation in (2), a gamma distribution to which the estimated value of the intensity function follows is obtained. Obtaining a probability distribution regarding this estimated value is the ultimate goal of intensity function estimation.
(4) Estimating hyperparameters necessary for estimating the intensity function from observed data based on the empirical Bayes method. Note that the empirical Bayes method is a method that uses hyperparameters that maximize the marginal likelihood as estimated values. A typical example of a hyperparameter is a parameter of a kernel function in a Gaussian process.
　図３は、図１に示される情報処理装置１の処理手順の一例を示すフローチャートである。図３において、プロセッサ１１は、ユーザによる、ガウス過程におけるカーネル関数の指定を受け付ける（ステップＳＳＴ２１）。次に、プロセッサ１１は、ユーザによる、等価カーネル関数の算出方法の指定を受け付ける（ステップＳＳＴ２２）。 FIG. 3 is a flowchart showing an example of the processing procedure of the information processing device 1 shown in FIG. In FIG. 3, the processor 11 accepts a user's designation of a kernel function in a Gaussian process (step SST21). Next, the processor 11 accepts the user's designation of the method for calculating the equivalent kernel function (step SST22).
　次に、プロセッサ１１は、指定されたカーネル関数および算出方法に基づいて、等価カーネル関数を算出する（ステップＳＴ２３）。さらに、プロセッサ１１は、算出された等価カーネル関数を利用して共変量に対する強度関数を推定する（ステップＳ２４）。 Next, the processor 11 calculates an equivalent kernel function based on the specified kernel function and calculation method (step ST23). Furthermore, the processor 11 estimates the intensity function for the covariate using the calculated equivalent kernel function (step S24).
　（詳細）
　次に、数式を参照して作用の詳細を説明する。 (detail)
Next, details of the operation will be explained with reference to mathematical formulas.
　［イベント発生データについて］
　解析対象であるイベントの発生位置に関するデータが入力として与えられる。イベント発生データは、以下の（Ａ），（Ｂ），（Ｃ）を含む。
Figure JPOXMLDOC01-appb-M000001
 　ただし、イベントが発生する空間の次元数は任意であり、例えば１次元であれば時間、２次元であれば地理空間、３次元であれば時空間などが考えられる。 [About event occurrence data]
Data regarding the occurrence position of the event to be analyzed is given as input. The event occurrence data includes the following (A), (B), and (C).
Figure JPOXMLDOC01-appb-M000001
 However, the number of dimensions of the space in which an event occurs is arbitrary; for example, one dimension may be time, two dimensions may be geographical space, and three dimensions may be space and time.
　［共変量データについて］
　イベントの観測領域Ｔ（式（Ｃ））内で観測された共変量のデータが、観測領域（式（Ｃ））内の任意の点（式（Ｄ））を入力として共変量を出力する関数（式（Ｅ））として与えられる。多くの応用例では、共変量に関する情報は観測領域（式（Ｃ））内の有限個の点上においてのみ得られる。その場合、回帰モデルやクリギングなどの補間技術を用いて関数（式（Ｅ））が構築されることを想定する。　
Figure JPOXMLDOC01-appb-M000002
 [About covariate data]
The covariate data observed within the event observation region T (formula (C)) is a function that outputs the covariate by inputting an arbitrary point (formula (D)) within the observation region (formula (C)). (Equation (E)). In many applications, information about the covariates is only available on a finite number of points within the observation region (Equation (C)). In that case, it is assumed that the function (formula (E)) is constructed using an interpolation technique such as a regression model or kriging.
Figure JPOXMLDOC01-appb-M000002
　［ガウス過程におけるカーネル関数の指定］について
　ガウス過程を利用するため、カーネル関数と呼ばれる、モデル化対象の関数の滑らかさを決める関数を指定する。関数に含まれるパラメータ（ハイパーパラメータ）の値も同時に指定する。　
　なお、実施形態におけるモデル化対象の関数とは、共変量に対する強度関数である。共変量空間における任意の二点（式（Ｆ））に対するカーネル関数を（式（Ｇ））と表記する。
Figure JPOXMLDOC01-appb-M000003
 [Specifying the kernel function in the Gaussian process] To use the Gaussian process, specify a function called the kernel function that determines the smoothness of the function to be modeled. Also specify the values of parameters (hyperparameters) included in the function.
Note that the function to be modeled in the embodiment is an intensity function for a covariate. The kernel function for arbitrary two points (formula (F)) in the covariate space is expressed as (formula (G)).
Figure JPOXMLDOC01-appb-M000003
　カーネル関数の例として、式（１）で与えられるガウスカーネルを挙げることができる。
Figure JPOXMLDOC01-appb-M000004
 An example of a kernel function is the Gaussian kernel given by equation (1).
Figure JPOXMLDOC01-appb-M000004
　または、カーネル関数の例として、有限次元の特徴写像ベクトル（式（Ｈ））の内積で表現される、式（２）のカーネルなどが挙げられる。
Figure JPOXMLDOC01-appb-M000005
 Alternatively, as an example of the kernel function, there may be mentioned the kernel of Equation (2), which is expressed by the inner product of a finite-dimensional feature mapping vector (Equation (H)).
Figure JPOXMLDOC01-appb-M000005
　［等価カーネル関数の算出方法の指定］について
　等価カーネル関数を算出する方法が入力として与えられる。等価カーネル関数を算出する方法は、算出方法の種類、およびモンテカルロ積分の点数（式（Ｉ））を含む。
Figure JPOXMLDOC01-appb-M000006
 Regarding [Specification of method for calculating equivalent kernel function] A method for calculating equivalent kernel function is given as input. The method for calculating the equivalent kernel function includes the type of calculation method and the Monte Carlo integration score (formula (I)).
Figure JPOXMLDOC01-appb-M000006
　なお、算出方法の種類の選択肢は１型、２型であり、２型はカーネル関数が有限次元の特徴写像ベクトルの内積で与えられる場合にのみ選択できるものとする。 Note that the options for the type of calculation method are type 1 and type 2, and type 2 can only be selected when the kernel function is given by the inner product of finite-dimensional feature mapping vectors.
　［強度関数の推定］について
　以上で与えられた情報をもとに、プロセッサ１１は等価カーネル関数（式（Ｊ））を算出する。
Figure JPOXMLDOC01-appb-M000007
 Regarding [Estimation of Intensity Function] Based on the information given above, the processor 11 calculates an equivalent kernel function (formula (J)).
Figure JPOXMLDOC01-appb-M000007
　そして、プロセッサ１１は、等価カーネル関数（Ｊ）を利用し、共変量に対する強度関数（式（Ｋ））を推定する。
Figure JPOXMLDOC01-appb-M000008
 Then, the processor 11 uses the equivalent kernel function (J) to estimate the intensity function (formula (K)) for the covariate.
Figure JPOXMLDOC01-appb-M000008
　まず、等価カーネル関数（式（Ｊ））は、式（３）の積分方程式の解として定義される。
Figure JPOXMLDOC01-appb-M000009
 First, the equivalent kernel function (Equation (J)) is defined as a solution to the integral equation of Equation (3).
Figure JPOXMLDOC01-appb-M000009
　上記積分方程式を数値的に解く準備として、積分部分をモンテカルロ積分で近似することにより式（４）を得る。
Figure JPOXMLDOC01-appb-M000010
 In preparation for numerically solving the above integral equation, equation (4) is obtained by approximating the integral part by Monte Carlo integration.
Figure JPOXMLDOC01-appb-M000010
　ただし、（式（Ｌ））はｍ番目のサンプル点上の共変量である。
Figure JPOXMLDOC01-appb-M000011
 However, (formula (L)) is a covariate on the m-th sample point.
Figure JPOXMLDOC01-appb-M000011
　算出方法の種類として１型が指定された場合、式（４）を縦ベクトル関数（式（Ｍ））に関する行列方程式として解くことで、式（５）のように等価カーネル関数（式（Ｎ））を得る。
Figure JPOXMLDOC01-appb-M000012
 When type 1 is specified as the type of calculation method, by solving equation (4) as a matrix equation regarding the vertical vector function (formula (M)), the equivalent kernel function (formula (N) ).
Figure JPOXMLDOC01-appb-M000012
　算出方法の種類として２型が指定された場合、カーネル関数が式（２）のように有限次元の特徴写像ベクトルの内積で与えられることを前提として、式（４）から等価カーネル関数（式（Ｏ））を式（６）の形で得る。
Figure JPOXMLDOC01-appb-M000013
 When Type 2 is specified as the type of calculation method, on the premise that the kernel function is given by the inner product of finite-dimensional feature mapping vectors as in Equation (2), the equivalent kernel function (Equation ( O)) is obtained in the form of equation (6).
Figure JPOXMLDOC01-appb-M000013
　次に、等価カーネル関数（式（Ｊ））を用いて強度関数の平方根のＭＡＰ推定値を式（７）で算出する。
Figure JPOXMLDOC01-appb-M000014
 Next, the MAP estimated value of the square root of the intensity function is calculated using equation (7) using the equivalent kernel function (formula (J)).
Figure JPOXMLDOC01-appb-M000014
　ただし、（式（Ｐ））は次の連立方程式（８）を解くことで得られる。
Figure JPOXMLDOC01-appb-M000015
 However, (Formula (P)) can be obtained by solving the following simultaneous equations (8).
Figure JPOXMLDOC01-appb-M000015
　次に、ラプラス近似のもと、強度関数の平方根がＭＡＰ推定値を平均とする正規分布に従うと仮定し、その共分散行列（式（Ｑ））を式（９）で算出する。
Figure JPOXMLDOC01-appb-M000016
 Next, based on the Laplace approximation, assuming that the square root of the intensity function follows a normal distribution with the MAP estimated value as the average, its covariance matrix (formula (Q)) is calculated using formula (9).
Figure JPOXMLDOC01-appb-M000016
　ただし、数（１０）が成り立つ。
Figure JPOXMLDOC01-appb-M000017
 However, the number (10) holds true.
Figure JPOXMLDOC01-appb-M000017
　最後に、各共変量値（式（Ｒ））における強度関数の推定値が従う確率分布は、尺度パラメータ（式（Ｓ））および形状パラメータ（式（Ｔ））が、それぞれ式（１１）で与えられるガンマ分布として算出される。
Figure JPOXMLDOC01-appb-M000018
 Finally, the probability distribution followed by the estimated value of the intensity function at each covariate value (formula (R)) is given by the scale parameter (formula (S)) and shape parameter (formula (T)) as shown in formula (11), respectively. It is calculated as the given gamma distribution.
Figure JPOXMLDOC01-appb-M000018
　なお、［強度関数の推定］の処理において、［ガウス過程におけるカーネル関数の指定］で指定されたハイパーパラメータの妥当性を周辺尤度関数に基づき評価することもできる。また、ハイパーパラメータを最適化する場合、周辺尤度関数を最大化するハイパーパラメータを探索し、その値を用いて式（１１）を再計算する。 Note that in the process of [estimation of intensity function], the validity of the hyperparameter specified in [specification of kernel function in Gaussian process] can also be evaluated based on the marginal likelihood function. Furthermore, when optimizing hyperparameters, a hyperparameter that maximizes the marginal likelihood function is searched for, and equation (11) is recalculated using that value.
　［推定された強度関数分布］について
　［強度関数の推定］で算出された強度関数の確率分布が出力される。出力されるものは、任意の共変量値（式（Ｒ））に対し、式（１１）で与えられる尺度および形状パラメータを持つガンマ分布の値を出力する関数である。 About [Estimated intensity function distribution] The probability distribution of the intensity function calculated in [Intensity function estimation] is output. What is output is a function that outputs, for any covariate value (formula (R)), a value of a gamma distribution with the scale and shape parameters given by formula (11).
　＜効果＞
　以上説明したように、実施形態によれば、ガウス過程を事前分布とするベイズ推定法を用いて、共変量に対する強度関数を推定することが可能になる。　
　なお、この発明は、上記実施形態そのままに限定されるものではなない。例えば、カーネル関数の選択は式（１）、または式（２）に限られるものではない。
　また、この発明は、実施段階では実施形態の要旨を逸脱しない範囲で構成要素を変形して具体化できる。さらに、上記実施形態に開示されている複数の構成要素の適宜な組み合せにより種々の発明を形成できる。例えば、実施形態に示される全構成要素から幾つかの構成要素を削除してもよい。さらに、異なる実施形態に亘る構成要素を適宜組み合せてもよい。 <Effect>
As described above, according to the embodiment, it is possible to estimate the intensity function for the covariate using the Bayesian estimation method using a Gaussian process as the prior distribution.
Note that the present invention is not limited to the above embodiments as they are. For example, the selection of the kernel function is not limited to equation (1) or equation (2).
Furthermore, the present invention can be embodied by modifying the constituent elements within the scope of the embodiments at the implementation stage. Furthermore, various inventions can be formed by appropriately combining the plurality of components disclosed in the above embodiments. For example, some components may be deleted from all the components shown in the embodiments. Furthermore, components from different embodiments may be combined as appropriate.
　１…情報処理装置
　２…入力装置
　３…出力装置
　１０…プログラム
　１１…プロセッサ
　１２…入出力インタフェース
　１３…記憶部
　１３１…第１記憶領域
　１３２…第２記憶領域
　１３３…第３記憶領域
　１００…イベント発生データ
　１０１…共変量データ
　１０２…カーネル関数指定部
　１０３…算出方法指定部
　１０５…強度関数分布
　１１２…強度関数推定部
　１１４…出力制御部。 1... Information processing device 2... Input device 3... Output device 10... Program 11... Processor 12... Input/output interface 13... Storage unit 131... First storage area 132... Second storage area 133... Third storage area 100... Event occurrence Data 101...Covariate data 102...Kernel function specification section 103...Calculation method specification section 105...Intensity function distribution 112...Intensity function estimation section 114...Output control section.

Claims (6)

  1. 　プロセッサおよび記憶部を備える情報処理装置において、
    　　前記記憶部は、
    　解析対象のイベントの発生位置に関するイベント発生データを記憶する第１記憶領域と、
    　前記イベントの観測領域内で観測された共変量データを記憶する第２記憶領域とを備え、
    　　前記プロセッサは、
    　ガウス過程におけるカーネル関数の指定を受け付けるカーネル関数指定部と、
    　等価カーネル関数の算出方法の指定を受け付ける算出方法指定部と、
    　前記指定されたカーネル関数および算出方法に基づいて前記等価カーネル関数を算出し、当該算出された等価カーネル関数を利用して共変量に対する強度関数を推定する強度関数推定部とを具備する、情報処理装置。     In an information processing device including a processor and a storage unit,
    The storage unit is
    a first storage area that stores event occurrence data regarding the occurrence position of the event to be analyzed;
    a second storage area for storing covariate data observed within the observation area of the event,
    The processor includes:
    a kernel function specification unit that accepts specification of a kernel function in a Gaussian process;
    a calculation method specification section that accepts a specification of a calculation method of the equivalent kernel function;
    and an intensity function estimator that calculates the equivalent kernel function based on the specified kernel function and calculation method, and estimates an intensity function for a covariate using the calculated equivalent kernel function. Device.
  2. 　前記イベント発生データは、観測されたイベントの回数と、イベント位置の系列と、観測領域とを少なくとも含む、請求項１に記載の情報処理装置。 The information processing device according to claim 1, wherein the event occurrence data includes at least the number of observed events, a series of event positions, and an observation area.
  3. 　前記カーネル関数指定部は、さらに、前記カーネル関数のハイパーパラメータの値の指定を受け付ける、請求項１に記載の情報処理装置。 The information processing device according to claim 1, wherein the kernel function designation unit further receives designation of a value of a hyperparameter of the kernel function.
  4. 　前記算出方法指定部は、少なくとも前記等価カーネル関数の算出方法の種類の指定、およびモンテカルロ積分の点数の指定を受け付ける、請求項１に記載の情報処理装置。 The information processing device according to claim 1, wherein the calculation method designation unit receives at least a designation of a type of calculation method for the equivalent kernel function and a designation of a Monte Carlo integration score.
  5. 　解析対象のイベントの発生位置に関するイベント発生データと前記イベントの観測領域内で観測された共変量データとを記憶する記憶部と、プロセッサとを備える情報処理装置の情報処理方法であって、
    　前記プロセッサが、ガウス過程におけるカーネル関数の指定を受け付ける過程と、
    　前記プロセッサが、等価カーネル関数の算出方法の指定を受け付ける過程と、
    　前記プロセッサが、前記指定されたカーネル関数および算出方法に基づいて前記等価カーネル関数を算出する過程と、
    　前記プロセッサが、前記算出された等価カーネル関数を利用して共変量に対する強度関数を推定する過程とを具備する、情報処理方法。     An information processing method for an information processing device, comprising: a storage unit that stores event occurrence data regarding the occurrence position of an event to be analyzed and covariate data observed within an observation area of the event; and a processor.
    a step in which the processor receives a specification of a kernel function in a Gaussian process;
    a step in which the processor receives a designation of a method for calculating an equivalent kernel function;
    a step in which the processor calculates the equivalent kernel function based on the specified kernel function and calculation method;
    An information processing method comprising: the processor estimating an intensity function for a covariate using the calculated equivalent kernel function.
  6. 　コンピュータを、請求項１乃至４のいずれか１項に記載の情報処理装置の前記各部として機能させる、プログラム。

          A program that causes a computer to function as each section of the information processing apparatus according to claim 4.
PCT/JP2022/021605 2022-05-26 2022-05-26 Information processing device, information processing method, and program WO2023228371A1 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
PCT/JP2022/021605 WO2023228371A1 (en) 2022-05-26 2022-05-26 Information processing device, information processing method, and program

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/JP2022/021605 WO2023228371A1 (en) 2022-05-26 2022-05-26 Information processing device, information processing method, and program

Publications (1)

Publication Number Publication Date
WO2023228371A1 true WO2023228371A1 (en) 2023-11-30

Family

ID=88918786

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/JP2022/021605 WO2023228371A1 (en) 2022-05-26 2022-05-26 Information processing device, information processing method, and program

Country Status (1)

Country Link
WO (1) WO2023228371A1 (en)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2020071750A (en) * 2018-11-01 2020-05-07 日本電信電話株式会社 Event prediction device, event prediction model and event prediction program
WO2021002008A1 (en) * 2019-07-04 2021-01-07 日本電信電話株式会社 Learning device, prediction device, learning method, prediction method, and program
WO2022097230A1 (en) * 2020-11-05 2022-05-12 日本電信電話株式会社 Prediction method, prediction device, and program

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2020071750A (en) * 2018-11-01 2020-05-07 日本電信電話株式会社 Event prediction device, event prediction model and event prediction program
WO2021002008A1 (en) * 2019-07-04 2021-01-07 日本電信電話株式会社 Learning device, prediction device, learning method, prediction method, and program
WO2022097230A1 (en) * 2020-11-05 2022-05-12 日本電信電話株式会社 Prediction method, prediction device, and program

Similar Documents

Publication Publication Date Title
Chen et al. Reduced rank regression via adaptive nuclear norm penalization
Kartal Koc et al. Model selection in multivariate adaptive regression splines (MARS) using information complexity as the fitness function
Kantas et al. Sequential Monte Carlo methods for high-dimensional inverse problems: A case study for the Navier--Stokes equations
Sauer Numerical solution of stochastic differential equations in finance
JP7061536B2 (en) Optimization device, simulation system and optimization method
Barnes et al. Considerate approaches to constructing summary statistics for ABC model selection
JP5988419B2 (en) Prediction method, prediction system, and program
Schneider et al. Learning stochastic closures using ensemble Kalman inversion
Peltola et al. Hierarchical Bayesian Survival Analysis and Projective Covariate Selection in Cardiovascular Event Risk Prediction.
JP7283065B2 (en) Estimation device, optimization device, estimation method, optimization method, and program
Perthame et al. Inverse regression approach to robust nonlinear high-to-low dimensional mapping
US10127694B2 (en) Enhanced triplet embedding and triplet creation for high-dimensional data visualizations
US20210300390A1 (en) Efficient computational inference using gaussian processes
Gu et al. Gaussian orthogonal latent factor processes for large incomplete matrices of correlated data
JP2013037471A (en) Probabilistic model update system, probabilistic model update device, probabilistic model update method, and program
Guan et al. Fast expectation-maximization algorithms for spatial generalized linear mixed models
WO2023228371A1 (en) Information processing device, information processing method, and program
JP7276482B2 (en) Knowledge tracing device, method and program
Korte-Stapff et al. A multivariate functional-data mixture model for spatio-temporal data: inference and cokriging
JP2023059866A (en) Information processing device, information processing method and program
JP7283574B2 (en) SPATIAL DATA RESOLUTION METHOD, SPATIAL DATA RESOLUTION APPARATUS, AND PROGRAM
Wang et al. Constrained spline regression in the presence of AR (p) errors
JP7047665B2 (en) Learning equipment, learning methods and learning programs
Finch Modeling high dimensional multilevel data using the lasso estimator: A simulation study
JP7133175B2 (en) SPATIAL DATA RESOLUTION APPARATUS, SPATIAL DATA RESOLUTION METHOD, AND SPATIAL DATA RESOLUTION PROGRAM

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 22943771

Country of ref document: EP

Kind code of ref document: A1